21M.1.AHL.TZ2.5

pestleMathematicsAIHLPaper 121M· sl-2-4-key-features-of-graphs-intersections-using-technologysource ↗

Roger buys a new laptop for himself at a cost of $£ 495$ . At the same time, he buys his daughter Chloe a higher specification laptop at a cost of $£ 2200$ .

It is anticipated that Roger’s laptop will depreciate at a rate of $10 %$ per year, whereas Chloe’s laptop will depreciate at a rate of $15 %$ per year.

Roger and Chloe’s laptops will have the same value $k$ years after they were purchased.

Estimate the value of Roger’s laptop after $5$ years.

[2]

Find the value of $k$ .

[2]

Comment on the validity of your answer to part (b).

[1]

Markscheme / solution

$£ 495 \times 0 . 9^{5} = £ 292 (£ 292.292 \dots)$ (M1)A1

[2 marks]

$£ 495 \times 0 . 9^{k} = 2200 \times 0 . 85^{k}$ (M1)

$k = 26.1 (26.0968 \dots)$ A1

Note: Award M1A0 for $k - 1$ in place of $k$ .

[2 marks]

depreciation rates unlikely to be constant (especially over a long time period) R1

Note: Accept reasonable answers based on the magnitude of $k$ or the fact that “value” depends on factors other than time.

[1 mark]

Examiners’ report

[N/A]